| Label |
Class |
Class size |
Class degree |
Base field |
Field degree |
Field signature |
Conductor |
Conductor norm |
Discriminant norm |
Root analytic conductor |
Bad primes |
Rank |
Torsion |
CM |
CM |
Sato-Tate |
$\Q$-curve |
Base change |
Semistable |
Potentially good |
Nonmax $\ell$ |
mod-$\ell$ images |
$Ш_{\textrm{an}}$ |
Tamagawa |
Regulator |
Period |
Leading coeff |
j-invariant |
Weierstrass coefficients |
Weierstrass equation |
| 4.1-a1 |
4.1-a |
$1$ |
$1$ |
4.4.19025.1 |
$4$ |
$[4, 0]$ |
4.1 |
\( 2^{2} \) |
\( 2^{6} \) |
$14.65745$ |
$(-1/2a^3+1/2a^2+4a+2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 3 \) |
$0.026060337$ |
$1168.666253$ |
2.649655722 |
\( \frac{18933}{16} a^{3} + \frac{2279}{4} a^{2} - \frac{198581}{16} a - \frac{30985}{2} \) |
\( \bigl[\frac{1}{2} a^{2} - \frac{1}{2} a - 3\) , \( \frac{1}{2} a^{3} - \frac{9}{2} a - 5\) , \( \frac{1}{2} a^{3} - \frac{7}{2} a - 4\) , \( \frac{43}{2} a^{3} - \frac{167}{2} a^{2} - 137 a + 575\) , \( -\frac{101}{2} a^{3} + 191 a^{2} + \frac{651}{2} a - 1302\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{2}-\frac{1}{2}a-3\right){x}{y}+\left(\frac{1}{2}a^{3}-\frac{7}{2}a-4\right){y}={x}^{3}+\left(\frac{1}{2}a^{3}-\frac{9}{2}a-5\right){x}^{2}+\left(\frac{43}{2}a^{3}-\frac{167}{2}a^{2}-137a+575\right){x}-\frac{101}{2}a^{3}+191a^{2}+\frac{651}{2}a-1302$ |
| 4.2-a1 |
4.2-a |
$1$ |
$1$ |
4.4.19025.1 |
$4$ |
$[4, 0]$ |
4.2 |
\( 2^{2} \) |
\( 2^{6} \) |
$14.65745$ |
$(1/2a^3-7/2a-1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 3 \) |
$0.026060337$ |
$1168.666253$ |
2.649655722 |
\( -\frac{18933}{16} a^{3} + \frac{65915}{16} a^{2} + \frac{61775}{8} a - \frac{104603}{4} \) |
\( \bigl[\frac{1}{2} a^{2} - \frac{1}{2} a - 3\) , \( -\frac{1}{2} a^{3} + \frac{9}{2} a + 3\) , \( \frac{1}{2} a^{3} - \frac{1}{2} a^{2} - 3 a\) , \( -23 a^{3} - 16 a^{2} + 250 a + 364\) , \( \frac{29}{2} a^{3} + 10 a^{2} - \frac{319}{2} a - 232\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{2}-\frac{1}{2}a-3\right){x}{y}+\left(\frac{1}{2}a^{3}-\frac{1}{2}a^{2}-3a\right){y}={x}^{3}+\left(-\frac{1}{2}a^{3}+\frac{9}{2}a+3\right){x}^{2}+\left(-23a^{3}-16a^{2}+250a+364\right){x}+\frac{29}{2}a^{3}+10a^{2}-\frac{319}{2}a-232$ |
| 5.1-a1 |
5.1-a |
$6$ |
$8$ |
4.4.19025.1 |
$4$ |
$[4, 0]$ |
5.1 |
\( 5 \) |
\( - 5^{8} \) |
$15.07204$ |
$(-1/2a^3+3/2a^2+3a-9)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$567.8627125$ |
2.058500724 |
\( -\frac{42864}{625} a^{3} - \frac{213383}{1250} a^{2} + \frac{1242843}{1250} a + \frac{235804}{125} \) |
\( \bigl[\frac{1}{2} a^{3} - \frac{9}{2} a - 3\) , \( -\frac{1}{2} a^{3} + \frac{1}{2} a^{2} + 4 a - 1\) , \( \frac{1}{2} a^{2} + \frac{1}{2} a - 3\) , \( -a^{3} - \frac{5}{2} a^{2} + \frac{29}{2} a + 37\) , \( -a^{3} - \frac{63}{2} a^{2} + \frac{37}{2} a + 240\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-\frac{9}{2}a-3\right){x}{y}+\left(\frac{1}{2}a^{2}+\frac{1}{2}a-3\right){y}={x}^{3}+\left(-\frac{1}{2}a^{3}+\frac{1}{2}a^{2}+4a-1\right){x}^{2}+\left(-a^{3}-\frac{5}{2}a^{2}+\frac{29}{2}a+37\right){x}-a^{3}-\frac{63}{2}a^{2}+\frac{37}{2}a+240$ |
| 5.1-a2 |
5.1-a |
$6$ |
$8$ |
4.4.19025.1 |
$4$ |
$[4, 0]$ |
5.1 |
\( 5 \) |
\( -5 \) |
$15.07204$ |
$(-1/2a^3+3/2a^2+3a-9)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 1 \) |
$1$ |
$283.9313562$ |
2.058500724 |
\( -\frac{26910632686262353944}{5} a^{3} - \frac{39783662428722626591}{10} a^{2} + \frac{118140358683388215391}{2} a + \frac{432270738100640157399}{5} \) |
\( \bigl[\frac{1}{2} a^{2} - \frac{1}{2} a - 3\) , \( \frac{1}{2} a^{3} - a^{2} - \frac{7}{2} a + 4\) , \( 1\) , \( 5 a^{3} + 3 a^{2} - 50 a - 62\) , \( -12 a^{3} - \frac{13}{2} a^{2} + \frac{295}{2} a + 217\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{2}-\frac{1}{2}a-3\right){x}{y}+{y}={x}^{3}+\left(\frac{1}{2}a^{3}-a^{2}-\frac{7}{2}a+4\right){x}^{2}+\left(5a^{3}+3a^{2}-50a-62\right){x}-12a^{3}-\frac{13}{2}a^{2}+\frac{295}{2}a+217$ |
| 5.1-a3 |
5.1-a |
$6$ |
$8$ |
4.4.19025.1 |
$4$ |
$[4, 0]$ |
5.1 |
\( 5 \) |
\( 5^{2} \) |
$15.07204$ |
$(-1/2a^3+3/2a^2+3a-9)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2 \) |
$1$ |
$2271.450850$ |
2.058500724 |
\( -\frac{2591968146}{5} a^{3} - \frac{3831867987}{10} a^{2} + \frac{56894997927}{10} a + 8327061734 \) |
\( \bigl[\frac{1}{2} a^{2} - \frac{1}{2} a - 3\) , \( \frac{1}{2} a^{3} - a^{2} - \frac{7}{2} a + 4\) , \( 1\) , \( -2 a^{2} + 13\) , \( -\frac{1}{2} a^{2} + \frac{3}{2} a + 7\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{2}-\frac{1}{2}a-3\right){x}{y}+{y}={x}^{3}+\left(\frac{1}{2}a^{3}-a^{2}-\frac{7}{2}a+4\right){x}^{2}+\left(-2a^{2}+13\right){x}-\frac{1}{2}a^{2}+\frac{3}{2}a+7$ |
| 5.1-a4 |
5.1-a |
$6$ |
$8$ |
4.4.19025.1 |
$4$ |
$[4, 0]$ |
5.1 |
\( 5 \) |
\( -5 \) |
$15.07204$ |
$(-1/2a^3+3/2a^2+3a-9)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$1135.725425$ |
2.058500724 |
\( \frac{5174574}{5} a^{3} + \frac{7100151}{10} a^{2} - \frac{14968923}{2} a - \frac{30985739}{5} \) |
\( \bigl[\frac{1}{2} a^{3} - \frac{1}{2} a^{2} - 4 a + 1\) , \( -a + 1\) , \( a + 1\) , \( -\frac{57}{2} a^{3} + 103 a^{2} + \frac{381}{2} a - 702\) , \( -\frac{665}{2} a^{3} + 1241 a^{2} + \frac{4345}{2} a - 8432\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-\frac{1}{2}a^{2}-4a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-\frac{57}{2}a^{3}+103a^{2}+\frac{381}{2}a-702\right){x}-\frac{665}{2}a^{3}+1241a^{2}+\frac{4345}{2}a-8432$ |
| 5.1-a5 |
5.1-a |
$6$ |
$8$ |
4.4.19025.1 |
$4$ |
$[4, 0]$ |
5.1 |
\( 5 \) |
\( 5^{4} \) |
$15.07204$ |
$(-1/2a^3+3/2a^2+3a-9)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2 \) |
$1$ |
$2271.450850$ |
2.058500724 |
\( -\frac{1458354}{25} a^{3} + \frac{12202387}{50} a^{2} + \frac{5351273}{50} a - \frac{4113671}{5} \) |
\( \bigl[1\) , \( \frac{1}{2} a^{3} - \frac{1}{2} a^{2} - 5 a\) , \( \frac{1}{2} a^{3} - \frac{1}{2} a^{2} - 4 a\) , \( \frac{53}{2} a^{3} + 10 a^{2} - \frac{549}{2} a - 362\) , \( -\frac{565}{2} a^{3} - \frac{383}{2} a^{2} + 3068 a + 4431\bigr] \) |
${y}^2+{x}{y}+\left(\frac{1}{2}a^{3}-\frac{1}{2}a^{2}-4a\right){y}={x}^{3}+\left(\frac{1}{2}a^{3}-\frac{1}{2}a^{2}-5a\right){x}^{2}+\left(\frac{53}{2}a^{3}+10a^{2}-\frac{549}{2}a-362\right){x}-\frac{565}{2}a^{3}-\frac{383}{2}a^{2}+3068a+4431$ |
| 5.1-a6 |
5.1-a |
$6$ |
$8$ |
4.4.19025.1 |
$4$ |
$[4, 0]$ |
5.1 |
\( 5 \) |
\( - 5^{2} \) |
$15.07204$ |
$(-1/2a^3+3/2a^2+3a-9)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$567.8627125$ |
2.058500724 |
\( -\frac{422630850474}{5} a^{3} + \frac{3872048742527}{10} a^{2} + \frac{997178407073}{10} a - 1441172749844 \) |
\( \bigl[1\) , \( \frac{1}{2} a^{3} - \frac{1}{2} a^{2} - 5 a\) , \( \frac{1}{2} a^{3} - \frac{1}{2} a^{2} - 4 a\) , \( \frac{63}{2} a^{3} - \frac{225}{2} a^{2} - 97 a + 343\) , \( -\frac{1599}{2} a^{3} + 723 a^{2} + \frac{12711}{2} a + 4662\bigr] \) |
${y}^2+{x}{y}+\left(\frac{1}{2}a^{3}-\frac{1}{2}a^{2}-4a\right){y}={x}^{3}+\left(\frac{1}{2}a^{3}-\frac{1}{2}a^{2}-5a\right){x}^{2}+\left(\frac{63}{2}a^{3}-\frac{225}{2}a^{2}-97a+343\right){x}-\frac{1599}{2}a^{3}+723a^{2}+\frac{12711}{2}a+4662$ |
| 5.1-b1 |
5.1-b |
$4$ |
$4$ |
4.4.19025.1 |
$4$ |
$[4, 0]$ |
5.1 |
\( 5 \) |
\( 5^{2} \) |
$15.07204$ |
$(-1/2a^3+3/2a^2+3a-9)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2 \) |
$1$ |
$719.0867168$ |
0.651671828 |
\( \frac{214041}{2} a^{3} - \frac{22673}{10} a^{2} - \frac{3927149}{5} a - \frac{125181}{5} \) |
\( \bigl[\frac{1}{2} a^{2} - \frac{1}{2} a - 4\) , \( \frac{1}{2} a^{2} - \frac{1}{2} a - 3\) , \( a\) , \( -2 a^{3} - 3 a^{2} + 12 a + 18\) , \( -\frac{17}{2} a^{3} - \frac{29}{2} a^{2} + 59 a + 101\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{2}-\frac{1}{2}a-4\right){x}{y}+a{y}={x}^{3}+\left(\frac{1}{2}a^{2}-\frac{1}{2}a-3\right){x}^{2}+\left(-2a^{3}-3a^{2}+12a+18\right){x}-\frac{17}{2}a^{3}-\frac{29}{2}a^{2}+59a+101$ |
| 5.1-b2 |
5.1-b |
$4$ |
$4$ |
4.4.19025.1 |
$4$ |
$[4, 0]$ |
5.1 |
\( 5 \) |
\( 5 \) |
$15.07204$ |
$(-1/2a^3+3/2a^2+3a-9)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$359.5433584$ |
0.651671828 |
\( \frac{1812245053283}{10} a^{3} + \frac{1287051346501}{10} a^{2} - 1305792085972 a - \frac{5567420494989}{5} \) |
\( \bigl[\frac{1}{2} a^{2} - \frac{1}{2} a - 4\) , \( \frac{1}{2} a^{2} - \frac{1}{2} a - 3\) , \( a\) , \( -37 a^{3} - \frac{121}{2} a^{2} + \frac{519}{2} a + 438\) , \( -\frac{1093}{2} a^{3} - \frac{1711}{2} a^{2} + 4049 a + 6754\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{2}-\frac{1}{2}a-4\right){x}{y}+a{y}={x}^{3}+\left(\frac{1}{2}a^{2}-\frac{1}{2}a-3\right){x}^{2}+\left(-37a^{3}-\frac{121}{2}a^{2}+\frac{519}{2}a+438\right){x}-\frac{1093}{2}a^{3}-\frac{1711}{2}a^{2}+4049a+6754$ |
| 5.1-b3 |
5.1-b |
$4$ |
$4$ |
4.4.19025.1 |
$4$ |
$[4, 0]$ |
5.1 |
\( 5 \) |
\( - 5^{4} \) |
$15.07204$ |
$(-1/2a^3+3/2a^2+3a-9)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$179.7716792$ |
0.651671828 |
\( -\frac{69127387}{50} a^{3} - \frac{51095401}{50} a^{2} + \frac{379340804}{25} a + \frac{555184097}{25} \) |
\( \bigl[\frac{1}{2} a^{2} - \frac{1}{2} a - 4\) , \( -a + 1\) , \( \frac{1}{2} a^{3} - \frac{7}{2} a - 4\) , \( -5 a^{3} + 19 a^{2} + 31 a - 127\) , \( \frac{85}{2} a^{3} - \frac{321}{2} a^{2} - 276 a + 1084\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{2}-\frac{1}{2}a-4\right){x}{y}+\left(\frac{1}{2}a^{3}-\frac{7}{2}a-4\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-5a^{3}+19a^{2}+31a-127\right){x}+\frac{85}{2}a^{3}-\frac{321}{2}a^{2}-276a+1084$ |
| 5.1-b4 |
5.1-b |
$4$ |
$4$ |
4.4.19025.1 |
$4$ |
$[4, 0]$ |
5.1 |
\( 5 \) |
\( -5 \) |
$15.07204$ |
$(-1/2a^3+3/2a^2+3a-9)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$359.5433584$ |
0.651671828 |
\( -\frac{7918073193}{10} a^{3} + \frac{36264353439}{10} a^{2} + 937487883 a - \frac{67519869641}{5} \) |
\( \bigl[\frac{1}{2} a^{3} - \frac{1}{2} a^{2} - 4 a + 1\) , \( -\frac{1}{2} a^{3} + \frac{1}{2} a^{2} + 4 a + 1\) , \( \frac{1}{2} a^{3} - \frac{1}{2} a^{2} - 3 a + 1\) , \( -3 a^{3} + 4 a^{2} + 26 a - 17\) , \( -a^{3} - 4 a^{2} + 15 a + 32\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-\frac{1}{2}a^{2}-4a+1\right){x}{y}+\left(\frac{1}{2}a^{3}-\frac{1}{2}a^{2}-3a+1\right){y}={x}^{3}+\left(-\frac{1}{2}a^{3}+\frac{1}{2}a^{2}+4a+1\right){x}^{2}+\left(-3a^{3}+4a^{2}+26a-17\right){x}-a^{3}-4a^{2}+15a+32$ |
| 5.2-a1 |
5.2-a |
$6$ |
$8$ |
4.4.19025.1 |
$4$ |
$[4, 0]$ |
5.2 |
\( 5 \) |
\( -5 \) |
$15.07204$ |
$(1/2a^3+1/2a^2-6a-9)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$1135.725425$ |
2.058500724 |
\( -\frac{5174574}{5} a^{3} + \frac{7629519}{2} a^{2} + \frac{29596869}{10} a - \frac{59683397}{5} \) |
\( \bigl[\frac{1}{2} a^{3} - \frac{9}{2} a - 3\) , \( 0\) , \( a\) , \( \frac{55}{2} a^{3} + 19 a^{2} - \frac{609}{2} a - 440\) , \( \frac{665}{2} a^{3} + \frac{487}{2} a^{2} - 3658 a - 5350\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-\frac{9}{2}a-3\right){x}{y}+a{y}={x}^{3}+\left(\frac{55}{2}a^{3}+19a^{2}-\frac{609}{2}a-440\right){x}+\frac{665}{2}a^{3}+\frac{487}{2}a^{2}-3658a-5350$ |
| 5.2-a2 |
5.2-a |
$6$ |
$8$ |
4.4.19025.1 |
$4$ |
$[4, 0]$ |
5.2 |
\( 5 \) |
\( 5^{4} \) |
$15.07204$ |
$(1/2a^3+1/2a^2-6a-9)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2 \) |
$1$ |
$2271.450850$ |
2.058500724 |
\( \frac{1458354}{25} a^{3} + \frac{3452263}{50} a^{2} - \frac{21005923}{50} a - \frac{13249879}{25} \) |
\( \bigl[\frac{1}{2} a^{2} - \frac{1}{2} a - 3\) , \( a - 1\) , \( \frac{1}{2} a^{3} - \frac{9}{2} a - 4\) , \( -\frac{29}{2} a^{3} - 3 a^{2} + \frac{205}{2} a + 39\) , \( \frac{153}{2} a^{3} + \frac{75}{2} a^{2} - 550 a - 356\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{2}-\frac{1}{2}a-3\right){x}{y}+\left(\frac{1}{2}a^{3}-\frac{9}{2}a-4\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-\frac{29}{2}a^{3}-3a^{2}+\frac{205}{2}a+39\right){x}+\frac{153}{2}a^{3}+\frac{75}{2}a^{2}-550a-356$ |
| 5.2-a3 |
5.2-a |
$6$ |
$8$ |
4.4.19025.1 |
$4$ |
$[4, 0]$ |
5.2 |
\( 5 \) |
\( -5 \) |
$15.07204$ |
$(1/2a^3+1/2a^2-6a-9)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 1 \) |
$1$ |
$283.9313562$ |
2.058500724 |
\( \frac{26910632686262353944}{5} a^{3} - \frac{40249491709259350051}{2} a^{2} - \frac{349670672441921700109}{10} a + \frac{680819170908487028637}{5} \) |
\( \bigl[\frac{1}{2} a^{2} - \frac{1}{2} a - 3\) , \( -\frac{1}{2} a^{3} + \frac{1}{2} a^{2} + 4 a\) , \( 1\) , \( -5 a^{3} + 18 a^{2} + 29 a - 104\) , \( 12 a^{3} - \frac{85}{2} a^{2} - \frac{197}{2} a + 346\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{2}-\frac{1}{2}a-3\right){x}{y}+{y}={x}^{3}+\left(-\frac{1}{2}a^{3}+\frac{1}{2}a^{2}+4a\right){x}^{2}+\left(-5a^{3}+18a^{2}+29a-104\right){x}+12a^{3}-\frac{85}{2}a^{2}-\frac{197}{2}a+346$ |
| 5.2-a4 |
5.2-a |
$6$ |
$8$ |
4.4.19025.1 |
$4$ |
$[4, 0]$ |
5.2 |
\( 5 \) |
\( 5^{2} \) |
$15.07204$ |
$(1/2a^3+1/2a^2-6a-9)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2 \) |
$1$ |
$2271.450850$ |
2.058500724 |
\( \frac{2591968146}{5} a^{3} - \frac{19383676863}{10} a^{2} - \frac{33679453077}{10} a + \frac{65574905494}{5} \) |
\( \bigl[\frac{1}{2} a^{2} - \frac{1}{2} a - 3\) , \( -\frac{1}{2} a^{3} + \frac{1}{2} a^{2} + 4 a\) , \( 1\) , \( -2 a^{2} + 4 a + 11\) , \( -\frac{1}{2} a^{2} - \frac{1}{2} a + 8\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{2}-\frac{1}{2}a-3\right){x}{y}+{y}={x}^{3}+\left(-\frac{1}{2}a^{3}+\frac{1}{2}a^{2}+4a\right){x}^{2}+\left(-2a^{2}+4a+11\right){x}-\frac{1}{2}a^{2}-\frac{1}{2}a+8$ |
| 5.2-a5 |
5.2-a |
$6$ |
$8$ |
4.4.19025.1 |
$4$ |
$[4, 0]$ |
5.2 |
\( 5 \) |
\( - 5^{8} \) |
$15.07204$ |
$(1/2a^3+1/2a^2-6a-9)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$567.8627125$ |
2.058500724 |
\( \frac{42864}{625} a^{3} - \frac{470567}{1250} a^{2} - \frac{558893}{1250} a + \frac{1650886}{625} \) |
\( \bigl[\frac{1}{2} a^{3} - \frac{1}{2} a^{2} - 4 a + 1\) , \( \frac{1}{2} a^{3} - a^{2} - \frac{9}{2} a + 4\) , \( \frac{1}{2} a^{2} + \frac{1}{2} a - 4\) , \( \frac{1}{2} a^{3} - \frac{9}{2} a^{2} - 5 a + 46\) , \( \frac{1}{2} a^{3} - \frac{67}{2} a^{2} + 50 a + 223\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-\frac{1}{2}a^{2}-4a+1\right){x}{y}+\left(\frac{1}{2}a^{2}+\frac{1}{2}a-4\right){y}={x}^{3}+\left(\frac{1}{2}a^{3}-a^{2}-\frac{9}{2}a+4\right){x}^{2}+\left(\frac{1}{2}a^{3}-\frac{9}{2}a^{2}-5a+46\right){x}+\frac{1}{2}a^{3}-\frac{67}{2}a^{2}+50a+223$ |
| 5.2-a6 |
5.2-a |
$6$ |
$8$ |
4.4.19025.1 |
$4$ |
$[4, 0]$ |
5.2 |
\( 5 \) |
\( - 5^{2} \) |
$15.07204$ |
$(1/2a^3+1/2a^2-6a-9)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$567.8627125$ |
2.058500724 |
\( \frac{422630850474}{5} a^{3} + \frac{1336263639683}{10} a^{2} - \frac{6205490789283}{10} a - \frac{5193881024894}{5} \) |
\( \bigl[1\) , \( -\frac{1}{2} a^{3} + a^{2} + \frac{9}{2} a - 5\) , \( \frac{1}{2} a^{3} - \frac{9}{2} a - 4\) , \( -32 a^{3} - \frac{35}{2} a^{2} + \frac{463}{2} a + 165\) , \( 800 a^{3} - 1676 a^{2} - 5408 a + 10941\bigr] \) |
${y}^2+{x}{y}+\left(\frac{1}{2}a^{3}-\frac{9}{2}a-4\right){y}={x}^{3}+\left(-\frac{1}{2}a^{3}+a^{2}+\frac{9}{2}a-5\right){x}^{2}+\left(-32a^{3}-\frac{35}{2}a^{2}+\frac{463}{2}a+165\right){x}+800a^{3}-1676a^{2}-5408a+10941$ |
| 5.2-b1 |
5.2-b |
$4$ |
$4$ |
4.4.19025.1 |
$4$ |
$[4, 0]$ |
5.2 |
\( 5 \) |
\( - 5^{4} \) |
$15.07204$ |
$(1/2a^3+1/2a^2-6a-9)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$179.7716792$ |
0.651671828 |
\( \frac{69127387}{50} a^{3} - \frac{129238781}{25} a^{2} - \frac{89821729}{10} a + \frac{874413507}{25} \) |
\( \bigl[\frac{1}{2} a^{2} - \frac{1}{2} a - 4\) , \( a\) , \( \frac{1}{2} a^{3} - \frac{1}{2} a^{2} - 3 a + 1\) , \( 5 a^{3} + \frac{7}{2} a^{2} - \frac{109}{2} a - 77\) , \( -43 a^{3} - \frac{65}{2} a^{2} + \frac{943}{2} a + 691\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{2}-\frac{1}{2}a-4\right){x}{y}+\left(\frac{1}{2}a^{3}-\frac{1}{2}a^{2}-3a+1\right){y}={x}^{3}+a{x}^{2}+\left(5a^{3}+\frac{7}{2}a^{2}-\frac{109}{2}a-77\right){x}-43a^{3}-\frac{65}{2}a^{2}+\frac{943}{2}a+691$ |
| 5.2-b2 |
5.2-b |
$4$ |
$4$ |
4.4.19025.1 |
$4$ |
$[4, 0]$ |
5.2 |
\( 5 \) |
\( -5 \) |
$15.07204$ |
$(1/2a^3+1/2a^2-6a-9)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$359.5433584$ |
0.651671828 |
\( \frac{7918073193}{10} a^{3} + 1251013386 a^{2} - \frac{58149366129}{10} a - \frac{48659290103}{5} \) |
\( \bigl[\frac{1}{2} a^{2} + \frac{1}{2} a - 4\) , \( \frac{1}{2} a^{2} - \frac{1}{2} a - 5\) , \( \frac{1}{2} a^{3} - \frac{1}{2} a^{2} - 4 a\) , \( -\frac{3}{2} a^{3} - 4 a^{2} + \frac{23}{2} a + 29\) , \( -\frac{15}{2} a^{3} - \frac{23}{2} a^{2} + 55 a + 89\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{2}+\frac{1}{2}a-4\right){x}{y}+\left(\frac{1}{2}a^{3}-\frac{1}{2}a^{2}-4a\right){y}={x}^{3}+\left(\frac{1}{2}a^{2}-\frac{1}{2}a-5\right){x}^{2}+\left(-\frac{3}{2}a^{3}-4a^{2}+\frac{23}{2}a+29\right){x}-\frac{15}{2}a^{3}-\frac{23}{2}a^{2}+55a+89$ |
| 5.2-b3 |
5.2-b |
$4$ |
$4$ |
4.4.19025.1 |
$4$ |
$[4, 0]$ |
5.2 |
\( 5 \) |
\( 5 \) |
$15.07204$ |
$(1/2a^3+1/2a^2-6a-9)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$359.5433584$ |
0.651671828 |
\( -\frac{1812245053283}{10} a^{3} + 672378650635 a^{2} + \frac{5047083006869}{10} a - \frac{10546732724957}{5} \) |
\( \bigl[\frac{1}{2} a^{2} - \frac{1}{2} a - 3\) , \( 0\) , \( a + 1\) , \( -\frac{35}{2} a^{3} + 60 a^{2} + \frac{289}{2} a - 487\) , \( \frac{411}{2} a^{3} - 794 a^{2} - \frac{2353}{2} a + 4954\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{2}-\frac{1}{2}a-3\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-\frac{35}{2}a^{3}+60a^{2}+\frac{289}{2}a-487\right){x}+\frac{411}{2}a^{3}-794a^{2}-\frac{2353}{2}a+4954$ |
| 5.2-b4 |
5.2-b |
$4$ |
$4$ |
4.4.19025.1 |
$4$ |
$[4, 0]$ |
5.2 |
\( 5 \) |
\( 5^{2} \) |
$15.07204$ |
$(1/2a^3+1/2a^2-6a-9)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2 \) |
$1$ |
$719.0867168$ |
0.651671828 |
\( -\frac{214041}{2} a^{3} + \frac{1593971}{5} a^{2} + \frac{4689029}{10} a - \frac{3528564}{5} \) |
\( \bigl[\frac{1}{2} a^{2} - \frac{1}{2} a - 3\) , \( 0\) , \( a + 1\) , \( -5 a^{3} + \frac{35}{2} a^{2} + \frac{69}{2} a - 122\) , \( -\frac{33}{2} a^{3} + 61 a^{2} + \frac{219}{2} a - 422\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{2}-\frac{1}{2}a-3\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-5a^{3}+\frac{35}{2}a^{2}+\frac{69}{2}a-122\right){x}-\frac{33}{2}a^{3}+61a^{2}+\frac{219}{2}a-422$ |
| 11.1-a1 |
11.1-a |
$2$ |
$2$ |
4.4.19025.1 |
$4$ |
$[4, 0]$ |
11.1 |
\( 11 \) |
\( 11^{10} \) |
$16.63317$ |
$(1/2a^3+3/2a^2-4a-11)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$129.0354932$ |
0.467753297 |
\( \frac{39441911126330}{25937424601} a^{3} - \frac{284427575711865}{51874849202} a^{2} - \frac{539202845978965}{51874849202} a + \frac{978155805520855}{25937424601} \) |
\( \bigl[\frac{1}{2} a^{3} - \frac{7}{2} a - 4\) , \( 1\) , \( \frac{1}{2} a^{3} - \frac{1}{2} a^{2} - 3 a\) , \( \frac{1}{2} a^{3} + \frac{5}{2} a^{2} - 3 a - 19\) , \( -\frac{1}{2} a^{3} - \frac{7}{2} a^{2} + 5 a + 24\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-\frac{7}{2}a-4\right){x}{y}+\left(\frac{1}{2}a^{3}-\frac{1}{2}a^{2}-3a\right){y}={x}^{3}+{x}^{2}+\left(\frac{1}{2}a^{3}+\frac{5}{2}a^{2}-3a-19\right){x}-\frac{1}{2}a^{3}-\frac{7}{2}a^{2}+5a+24$ |
| 11.1-a2 |
11.1-a |
$2$ |
$2$ |
4.4.19025.1 |
$4$ |
$[4, 0]$ |
11.1 |
\( 11 \) |
\( 11^{5} \) |
$16.63317$ |
$(1/2a^3+3/2a^2-4a-11)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$258.0709865$ |
0.467753297 |
\( \frac{7445658704170}{161051} a^{3} - \frac{55789230024735}{322102} a^{2} - \frac{96642294911435}{322102} a + \frac{188880598101870}{161051} \) |
\( \bigl[\frac{1}{2} a^{3} - \frac{9}{2} a - 3\) , \( -\frac{1}{2} a^{3} + a^{2} + \frac{7}{2} a - 3\) , \( \frac{1}{2} a^{3} - \frac{1}{2} a^{2} - 4 a\) , \( 360 a^{3} - \frac{1373}{2} a^{2} - \frac{4395}{2} a + 147\) , \( \frac{19697}{2} a^{3} - 19315 a^{2} - \frac{118269}{2} a + 7384\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-\frac{9}{2}a-3\right){x}{y}+\left(\frac{1}{2}a^{3}-\frac{1}{2}a^{2}-4a\right){y}={x}^{3}+\left(-\frac{1}{2}a^{3}+a^{2}+\frac{7}{2}a-3\right){x}^{2}+\left(360a^{3}-\frac{1373}{2}a^{2}-\frac{4395}{2}a+147\right){x}+\frac{19697}{2}a^{3}-19315a^{2}-\frac{118269}{2}a+7384$ |
| 11.1-b1 |
11.1-b |
$2$ |
$2$ |
4.4.19025.1 |
$4$ |
$[4, 0]$ |
11.1 |
\( 11 \) |
\( 11^{3} \) |
$16.63317$ |
$(1/2a^3+3/2a^2-4a-11)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 3 \) |
$0.341413160$ |
$424.1049805$ |
3.149289259 |
\( -\frac{46331656}{1331} a^{3} + \frac{76551529}{2662} a^{2} + \frac{723766449}{2662} a + \frac{380243862}{1331} \) |
\( \bigl[\frac{1}{2} a^{3} - \frac{7}{2} a - 4\) , \( -\frac{1}{2} a^{3} + a^{2} + \frac{7}{2} a - 5\) , \( \frac{1}{2} a^{2} + \frac{1}{2} a - 4\) , \( -\frac{69}{2} a^{3} + 128 a^{2} + \frac{453}{2} a - 863\) , \( -\frac{575}{2} a^{3} + 1076 a^{2} + \frac{3741}{2} a - 7285\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-\frac{7}{2}a-4\right){x}{y}+\left(\frac{1}{2}a^{2}+\frac{1}{2}a-4\right){y}={x}^{3}+\left(-\frac{1}{2}a^{3}+a^{2}+\frac{7}{2}a-5\right){x}^{2}+\left(-\frac{69}{2}a^{3}+128a^{2}+\frac{453}{2}a-863\right){x}-\frac{575}{2}a^{3}+1076a^{2}+\frac{3741}{2}a-7285$ |
| 11.1-b2 |
11.1-b |
$2$ |
$2$ |
4.4.19025.1 |
$4$ |
$[4, 0]$ |
11.1 |
\( 11 \) |
\( - 11^{6} \) |
$16.63317$ |
$(1/2a^3+3/2a^2-4a-11)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \cdot 3 \) |
$0.682826320$ |
$106.0262451$ |
3.149289259 |
\( \frac{218928385}{1771561} a^{3} + \frac{554397615}{3543122} a^{2} - \frac{3247729395}{3543122} a - \frac{2514103577}{1771561} \) |
\( \bigl[1\) , \( \frac{1}{2} a^{3} - a^{2} - \frac{9}{2} a + 3\) , \( \frac{1}{2} a^{3} - \frac{1}{2} a^{2} - 4 a\) , \( -\frac{9}{2} a^{3} - \frac{17}{2} a^{2} + 36 a + 73\) , \( -\frac{13}{2} a^{3} - 12 a^{2} + \frac{91}{2} a + 85\bigr] \) |
${y}^2+{x}{y}+\left(\frac{1}{2}a^{3}-\frac{1}{2}a^{2}-4a\right){y}={x}^{3}+\left(\frac{1}{2}a^{3}-a^{2}-\frac{9}{2}a+3\right){x}^{2}+\left(-\frac{9}{2}a^{3}-\frac{17}{2}a^{2}+36a+73\right){x}-\frac{13}{2}a^{3}-12a^{2}+\frac{91}{2}a+85$ |
| 11.1-c1 |
11.1-c |
$2$ |
$2$ |
4.4.19025.1 |
$4$ |
$[4, 0]$ |
11.1 |
\( 11 \) |
\( 11^{2} \) |
$16.63317$ |
$(1/2a^3+3/2a^2-4a-11)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$418.3261536$ |
1.516431122 |
\( \frac{939885469}{242} a^{3} - \frac{1757211473}{121} a^{2} - \frac{6106712349}{242} a + \frac{11890006588}{121} \) |
\( \bigl[\frac{1}{2} a^{3} - \frac{7}{2} a - 4\) , \( -\frac{1}{2} a^{2} + \frac{1}{2} a + 5\) , \( \frac{1}{2} a^{3} - \frac{7}{2} a - 4\) , \( -15 a^{3} - \frac{49}{2} a^{2} + \frac{223}{2} a + 191\) , \( 391 a^{3} + \frac{1235}{2} a^{2} - \frac{5741}{2} a - 4803\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-\frac{7}{2}a-4\right){x}{y}+\left(\frac{1}{2}a^{3}-\frac{7}{2}a-4\right){y}={x}^{3}+\left(-\frac{1}{2}a^{2}+\frac{1}{2}a+5\right){x}^{2}+\left(-15a^{3}-\frac{49}{2}a^{2}+\frac{223}{2}a+191\right){x}+391a^{3}+\frac{1235}{2}a^{2}-\frac{5741}{2}a-4803$ |
| 11.1-c2 |
11.1-c |
$2$ |
$2$ |
4.4.19025.1 |
$4$ |
$[4, 0]$ |
11.1 |
\( 11 \) |
\( 11 \) |
$16.63317$ |
$(1/2a^3+3/2a^2-4a-11)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$836.6523072$ |
1.516431122 |
\( -\frac{69726171}{22} a^{3} + \frac{160640687}{11} a^{2} + \frac{80577361}{22} a - \frac{599123687}{11} \) |
\( \bigl[\frac{1}{2} a^{3} - \frac{1}{2} a^{2} - 3 a + 1\) , \( \frac{1}{2} a^{3} - a^{2} - \frac{5}{2} a + 3\) , \( \frac{1}{2} a^{3} - \frac{1}{2} a^{2} - 3 a + 1\) , \( -27 a^{3} + 112 a^{2} + 174 a - 762\) , \( -268 a^{3} + 1026 a^{2} + 1738 a - 6951\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-\frac{1}{2}a^{2}-3a+1\right){x}{y}+\left(\frac{1}{2}a^{3}-\frac{1}{2}a^{2}-3a+1\right){y}={x}^{3}+\left(\frac{1}{2}a^{3}-a^{2}-\frac{5}{2}a+3\right){x}^{2}+\left(-27a^{3}+112a^{2}+174a-762\right){x}-268a^{3}+1026a^{2}+1738a-6951$ |
| 11.2-a1 |
11.2-a |
$2$ |
$2$ |
4.4.19025.1 |
$4$ |
$[4, 0]$ |
11.2 |
\( 11 \) |
\( 11^{5} \) |
$16.63317$ |
$(-3/2a^2+5/2a+10)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$258.0709865$ |
0.467753297 |
\( -\frac{7445658704170}{161051} a^{3} - \frac{11115277799715}{322102} a^{2} + \frac{163546802735885}{322102} a + \frac{10919135848905}{14641} \) |
\( \bigl[\frac{1}{2} a^{3} - \frac{1}{2} a^{2} - 4 a + 1\) , \( \frac{1}{2} a^{3} - \frac{1}{2} a^{2} - 5 a - 1\) , \( \frac{1}{2} a^{2} - \frac{1}{2} a - 3\) , \( -361 a^{3} + 394 a^{2} + 2499 a - 2374\) , \( -9488 a^{3} + \frac{19673}{2} a^{2} + \frac{131449}{2} a - 58840\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-\frac{1}{2}a^{2}-4a+1\right){x}{y}+\left(\frac{1}{2}a^{2}-\frac{1}{2}a-3\right){y}={x}^{3}+\left(\frac{1}{2}a^{3}-\frac{1}{2}a^{2}-5a-1\right){x}^{2}+\left(-361a^{3}+394a^{2}+2499a-2374\right){x}-9488a^{3}+\frac{19673}{2}a^{2}+\frac{131449}{2}a-58840$ |
| 11.2-a2 |
11.2-a |
$2$ |
$2$ |
4.4.19025.1 |
$4$ |
$[4, 0]$ |
11.2 |
\( 11 \) |
\( 11^{10} \) |
$16.63317$ |
$(-3/2a^2+5/2a+10)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$129.0354932$ |
0.467753297 |
\( -\frac{39441911126330}{25937424601} a^{3} - \frac{47776108953885}{51874849202} a^{2} + \frac{871406530644715}{51874849202} a + \frac{55071136891070}{2357947691} \) |
\( \bigl[\frac{1}{2} a^{3} - \frac{1}{2} a^{2} - 3 a + 1\) , \( -\frac{1}{2} a^{3} + \frac{1}{2} a^{2} + 5 a - 1\) , \( \frac{1}{2} a^{3} - \frac{9}{2} a - 4\) , \( \frac{3}{2} a^{3} + a^{2} - \frac{21}{2} a - 8\) , \( 5 a^{3} - \frac{17}{2} a^{2} - \frac{43}{2} a + 11\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-\frac{1}{2}a^{2}-3a+1\right){x}{y}+\left(\frac{1}{2}a^{3}-\frac{9}{2}a-4\right){y}={x}^{3}+\left(-\frac{1}{2}a^{3}+\frac{1}{2}a^{2}+5a-1\right){x}^{2}+\left(\frac{3}{2}a^{3}+a^{2}-\frac{21}{2}a-8\right){x}+5a^{3}-\frac{17}{2}a^{2}-\frac{43}{2}a+11$ |
| 11.2-b1 |
11.2-b |
$2$ |
$2$ |
4.4.19025.1 |
$4$ |
$[4, 0]$ |
11.2 |
\( 11 \) |
\( - 11^{6} \) |
$16.63317$ |
$(-3/2a^2+5/2a+10)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \cdot 3 \) |
$0.682826320$ |
$106.0262451$ |
3.149289259 |
\( -\frac{218928385}{1771561} a^{3} + \frac{1867967925}{3543122} a^{2} + \frac{825363855}{3543122} a - \frac{331076462}{161051} \) |
\( \bigl[\frac{1}{2} a^{2} - \frac{1}{2} a - 4\) , \( -\frac{1}{2} a^{2} - \frac{1}{2} a + 5\) , \( \frac{1}{2} a^{3} - \frac{7}{2} a - 3\) , \( a^{3} - \frac{7}{2} a^{2} - \frac{9}{2} a + 16\) , \( a^{3} - 7 a^{2} + 29\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{2}-\frac{1}{2}a-4\right){x}{y}+\left(\frac{1}{2}a^{3}-\frac{7}{2}a-3\right){y}={x}^{3}+\left(-\frac{1}{2}a^{2}-\frac{1}{2}a+5\right){x}^{2}+\left(a^{3}-\frac{7}{2}a^{2}-\frac{9}{2}a+16\right){x}+a^{3}-7a^{2}+29$ |
| 11.2-b2 |
11.2-b |
$2$ |
$2$ |
4.4.19025.1 |
$4$ |
$[4, 0]$ |
11.2 |
\( 11 \) |
\( 11^{3} \) |
$16.63317$ |
$(-3/2a^2+5/2a+10)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 3 \) |
$0.341413160$ |
$424.1049805$ |
3.149289259 |
\( \frac{46331656}{1331} a^{3} - \frac{201438407}{2662} a^{2} - \frac{598879571}{2662} a + \frac{66733745}{121} \) |
\( \bigl[\frac{1}{2} a^{3} - \frac{1}{2} a^{2} - 3 a + 1\) , \( a\) , \( \frac{1}{2} a^{3} - \frac{7}{2} a - 3\) , \( \frac{73}{2} a^{3} + \frac{55}{2} a^{2} - 393 a - 575\) , \( 386 a^{3} + \frac{575}{2} a^{2} - \frac{8451}{2} a - 6188\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-\frac{1}{2}a^{2}-3a+1\right){x}{y}+\left(\frac{1}{2}a^{3}-\frac{7}{2}a-3\right){y}={x}^{3}+a{x}^{2}+\left(\frac{73}{2}a^{3}+\frac{55}{2}a^{2}-393a-575\right){x}+386a^{3}+\frac{575}{2}a^{2}-\frac{8451}{2}a-6188$ |
| 11.2-c1 |
11.2-c |
$2$ |
$2$ |
4.4.19025.1 |
$4$ |
$[4, 0]$ |
11.2 |
\( 11 \) |
\( 11 \) |
$16.63317$ |
$(-3/2a^2+5/2a+10)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$836.6523072$ |
1.516431122 |
\( \frac{69726171}{22} a^{3} + \frac{112102861}{22} a^{2} - \frac{256980798}{11} a - 39368855 \) |
\( \bigl[\frac{1}{2} a^{3} - \frac{7}{2} a - 4\) , \( \frac{1}{2} a^{3} - \frac{9}{2} a - 3\) , \( \frac{1}{2} a^{2} - \frac{1}{2} a - 4\) , \( \frac{63}{2} a^{3} + \frac{51}{2} a^{2} - 338 a - 498\) , \( 227 a^{3} + 171 a^{2} - 2478 a - 3633\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-\frac{7}{2}a-4\right){x}{y}+\left(\frac{1}{2}a^{2}-\frac{1}{2}a-4\right){y}={x}^{3}+\left(\frac{1}{2}a^{3}-\frac{9}{2}a-3\right){x}^{2}+\left(\frac{63}{2}a^{3}+\frac{51}{2}a^{2}-338a-498\right){x}+227a^{3}+171a^{2}-2478a-3633$ |
| 11.2-c2 |
11.2-c |
$2$ |
$2$ |
4.4.19025.1 |
$4$ |
$[4, 0]$ |
11.2 |
\( 11 \) |
\( 11^{2} \) |
$16.63317$ |
$(-3/2a^2+5/2a+10)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$418.3261536$ |
1.516431122 |
\( -\frac{939885469}{242} a^{3} - \frac{694766539}{242} a^{2} + \frac{5157950917}{121} a + \frac{686307425}{11} \) |
\( \bigl[\frac{1}{2} a^{2} + \frac{1}{2} a - 4\) , \( -\frac{1}{2} a^{2} - \frac{1}{2} a + 4\) , \( 0\) , \( 3 a^{3} - \frac{25}{2} a^{2} - \frac{17}{2} a + 53\) , \( -22 a^{3} + \frac{203}{2} a^{2} + \frac{45}{2} a - 372\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{2}+\frac{1}{2}a-4\right){x}{y}={x}^{3}+\left(-\frac{1}{2}a^{2}-\frac{1}{2}a+4\right){x}^{2}+\left(3a^{3}-\frac{25}{2}a^{2}-\frac{17}{2}a+53\right){x}-22a^{3}+\frac{203}{2}a^{2}+\frac{45}{2}a-372$ |
| 20.1-a1 |
20.1-a |
$4$ |
$6$ |
4.4.19025.1 |
$4$ |
$[4, 0]$ |
20.1 |
\( 2^{2} \cdot 5 \) |
\( - 2^{4} \cdot 5 \) |
$17.92378$ |
$(-1/2a^3+3/2a^2+3a-9), (1/2a^3-7/2a-1)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2 \) |
$1.283184350$ |
$1445.171896$ |
2.987677491 |
\( \frac{3047}{40} a^{3} + \frac{1130529}{40} a^{2} - \frac{132281}{4} a - \frac{1221473}{10} \) |
\( \bigl[\frac{1}{2} a^{3} - \frac{7}{2} a - 4\) , \( \frac{1}{2} a^{3} - a^{2} - \frac{7}{2} a + 5\) , \( \frac{1}{2} a^{3} - \frac{9}{2} a - 3\) , \( -\frac{7}{2} a^{2} + \frac{25}{2} a + 43\) , \( -5 a^{3} - 8 a^{2} + 76 a + 135\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-\frac{7}{2}a-4\right){x}{y}+\left(\frac{1}{2}a^{3}-\frac{9}{2}a-3\right){y}={x}^{3}+\left(\frac{1}{2}a^{3}-a^{2}-\frac{7}{2}a+5\right){x}^{2}+\left(-\frac{7}{2}a^{2}+\frac{25}{2}a+43\right){x}-5a^{3}-8a^{2}+76a+135$ |
| 20.1-a2 |
20.1-a |
$4$ |
$6$ |
4.4.19025.1 |
$4$ |
$[4, 0]$ |
20.1 |
\( 2^{2} \cdot 5 \) |
\( - 2^{12} \cdot 5^{3} \) |
$17.92378$ |
$(-1/2a^3+3/2a^2+3a-9), (1/2a^3-7/2a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2 \cdot 3 \) |
$3.849553050$ |
$17.84162835$ |
2.987677491 |
\( -\frac{193066453992715621}{1600} a^{3} + \frac{442116976490500419}{800} a^{2} + \frac{11429398180028347}{80} a - \frac{51448046581033861}{25} \) |
\( \bigl[\frac{1}{2} a^{3} - \frac{7}{2} a - 4\) , \( \frac{1}{2} a^{3} - a^{2} - \frac{7}{2} a + 5\) , \( \frac{1}{2} a^{3} - \frac{9}{2} a - 3\) , \( \frac{145}{2} a^{3} - \frac{327}{2} a^{2} - 390 a + 208\) , \( \frac{1941}{2} a^{3} - 2209 a^{2} - \frac{10503}{2} a + 2658\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-\frac{7}{2}a-4\right){x}{y}+\left(\frac{1}{2}a^{3}-\frac{9}{2}a-3\right){y}={x}^{3}+\left(\frac{1}{2}a^{3}-a^{2}-\frac{7}{2}a+5\right){x}^{2}+\left(\frac{145}{2}a^{3}-\frac{327}{2}a^{2}-390a+208\right){x}+\frac{1941}{2}a^{3}-2209a^{2}-\frac{10503}{2}a+2658$ |
| 20.1-a3 |
20.1-a |
$4$ |
$6$ |
4.4.19025.1 |
$4$ |
$[4, 0]$ |
20.1 |
\( 2^{2} \cdot 5 \) |
\( - 2^{24} \cdot 5^{6} \) |
$17.92378$ |
$(-1/2a^3+3/2a^2+3a-9), (1/2a^3-7/2a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{3} \cdot 3 \) |
$1.924776525$ |
$8.920814175$ |
2.987677491 |
\( \frac{479955202289}{256000} a^{3} - \frac{4990176723243}{512000} a^{2} - \frac{21699491587}{256000} a + \frac{5017061059949}{128000} \) |
\( \bigl[1\) , \( 0\) , \( \frac{1}{2} a^{3} - \frac{9}{2} a - 3\) , \( 2 a^{3} + 27 a^{2} - 18 a - 192\) , \( -536 a^{3} - 149 a^{2} + 3824 a + 1653\bigr] \) |
${y}^2+{x}{y}+\left(\frac{1}{2}a^{3}-\frac{9}{2}a-3\right){y}={x}^{3}+\left(2a^{3}+27a^{2}-18a-192\right){x}-536a^{3}-149a^{2}+3824a+1653$ |
| 20.1-a4 |
20.1-a |
$4$ |
$6$ |
4.4.19025.1 |
$4$ |
$[4, 0]$ |
20.1 |
\( 2^{2} \cdot 5 \) |
\( - 2^{8} \cdot 5^{2} \) |
$17.92378$ |
$(-1/2a^3+3/2a^2+3a-9), (1/2a^3-7/2a-1)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{3} \) |
$0.641592175$ |
$722.5859482$ |
2.987677491 |
\( -\frac{24871}{160} a^{3} - \frac{4011}{32} a^{2} + \frac{137441}{80} a + \frac{103011}{40} \) |
\( \bigl[1\) , \( 0\) , \( \frac{1}{2} a^{3} - \frac{9}{2} a - 3\) , \( -\frac{1}{2} a^{3} - 3 a^{2} + \frac{9}{2} a + 23\) , \( 20 a^{3} + 6 a^{2} - 144 a - 68\bigr] \) |
${y}^2+{x}{y}+\left(\frac{1}{2}a^{3}-\frac{9}{2}a-3\right){y}={x}^{3}+\left(-\frac{1}{2}a^{3}-3a^{2}+\frac{9}{2}a+23\right){x}+20a^{3}+6a^{2}-144a-68$ |
| 20.1-b1 |
20.1-b |
$6$ |
$8$ |
4.4.19025.1 |
$4$ |
$[4, 0]$ |
20.1 |
\( 2^{2} \cdot 5 \) |
\( 2^{2} \cdot 5^{16} \) |
$17.92378$ |
$(-1/2a^3+3/2a^2+3a-9), (1/2a^3-7/2a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$16$ |
\( 2^{4} \) |
$1$ |
$2.332012944$ |
1.082053160 |
\( -\frac{15480776488356189}{781250} a^{3} + \frac{14257211863146797}{156250} a^{2} + \frac{15890015554392443}{781250} a - \frac{130113053600209417}{390625} \) |
\( \bigl[\frac{1}{2} a^{3} - \frac{7}{2} a - 4\) , \( \frac{1}{2} a^{3} - \frac{1}{2} a^{2} - 4 a + 1\) , \( \frac{1}{2} a^{2} + \frac{1}{2} a - 3\) , \( -\frac{153}{2} a^{3} + 253 a^{2} + \frac{1019}{2} a - 1693\) , \( -\frac{2351}{2} a^{3} + \frac{8143}{2} a^{2} + 7695 a - 27455\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-\frac{7}{2}a-4\right){x}{y}+\left(\frac{1}{2}a^{2}+\frac{1}{2}a-3\right){y}={x}^{3}+\left(\frac{1}{2}a^{3}-\frac{1}{2}a^{2}-4a+1\right){x}^{2}+\left(-\frac{153}{2}a^{3}+253a^{2}+\frac{1019}{2}a-1693\right){x}-\frac{2351}{2}a^{3}+\frac{8143}{2}a^{2}+7695a-27455$ |
| 20.1-b2 |
20.1-b |
$6$ |
$8$ |
4.4.19025.1 |
$4$ |
$[4, 0]$ |
20.1 |
\( 2^{2} \cdot 5 \) |
\( 2^{4} \cdot 5^{8} \) |
$17.92378$ |
$(-1/2a^3+3/2a^2+3a-9), (1/2a^3-7/2a-1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$4$ |
\( 2^{4} \) |
$1$ |
$37.31220711$ |
1.082053160 |
\( \frac{1122734920106877}{625} a^{3} + \frac{7095442979584977}{2500} a^{2} - \frac{8245228518647391}{625} a - \frac{13799184802490311}{625} \) |
\( \bigl[\frac{1}{2} a^{3} - \frac{7}{2} a - 4\) , \( \frac{1}{2} a^{3} - \frac{1}{2} a^{2} - 4 a + 1\) , \( \frac{1}{2} a^{2} + \frac{1}{2} a - 3\) , \( -9 a^{3} + 8 a^{2} + 62 a - 48\) , \( -82 a^{3} - \frac{29}{2} a^{2} + \frac{1169}{2} a + 196\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-\frac{7}{2}a-4\right){x}{y}+\left(\frac{1}{2}a^{2}+\frac{1}{2}a-3\right){y}={x}^{3}+\left(\frac{1}{2}a^{3}-\frac{1}{2}a^{2}-4a+1\right){x}^{2}+\left(-9a^{3}+8a^{2}+62a-48\right){x}-82a^{3}-\frac{29}{2}a^{2}+\frac{1169}{2}a+196$ |
| 20.1-b3 |
20.1-b |
$6$ |
$8$ |
4.4.19025.1 |
$4$ |
$[4, 0]$ |
20.1 |
\( 2^{2} \cdot 5 \) |
\( 2^{2} \cdot 5^{4} \) |
$17.92378$ |
$(-1/2a^3+3/2a^2+3a-9), (1/2a^3-7/2a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$64$ |
\( 2^{2} \) |
$1$ |
$2.332012944$ |
1.082053160 |
\( \frac{4444803347644929486122189493}{50} a^{3} + \frac{7022549713364439131619323879}{50} a^{2} - \frac{32642094062571182914537058147}{50} a - \frac{27314845230329169478044854703}{25} \) |
\( \bigl[\frac{1}{2} a^{3} - \frac{7}{2} a - 4\) , \( \frac{1}{2} a^{3} - \frac{1}{2} a^{2} - 4 a + 1\) , \( \frac{1}{2} a^{2} + \frac{1}{2} a - 3\) , \( -\frac{203}{2} a^{3} - 157 a^{2} + \frac{1469}{2} a + 1197\) , \( -\frac{5333}{2} a^{3} - \frac{8017}{2} a^{2} + 19520 a + 31251\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-\frac{7}{2}a-4\right){x}{y}+\left(\frac{1}{2}a^{2}+\frac{1}{2}a-3\right){y}={x}^{3}+\left(\frac{1}{2}a^{3}-\frac{1}{2}a^{2}-4a+1\right){x}^{2}+\left(-\frac{203}{2}a^{3}-157a^{2}+\frac{1469}{2}a+1197\right){x}-\frac{5333}{2}a^{3}-\frac{8017}{2}a^{2}+19520a+31251$ |
| 20.1-b4 |
20.1-b |
$6$ |
$8$ |
4.4.19025.1 |
$4$ |
$[4, 0]$ |
20.1 |
\( 2^{2} \cdot 5 \) |
\( 2^{16} \cdot 5^{2} \) |
$17.92378$ |
$(-1/2a^3+3/2a^2+3a-9), (1/2a^3-7/2a-1)$ |
0 |
$\Z/8\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$596.9953138$ |
1.082053160 |
\( \frac{4703481}{128} a^{3} - \frac{171607247}{1280} a^{2} - \frac{167405831}{640} a + \frac{309351913}{320} \) |
\( \bigl[\frac{1}{2} a^{3} - \frac{7}{2} a - 4\) , \( -\frac{1}{2} a^{2} + \frac{3}{2} a + 3\) , \( \frac{1}{2} a^{3} - \frac{1}{2} a^{2} - 3 a\) , \( \frac{11}{2} a^{3} - 3 a^{2} - \frac{83}{2} a - 34\) , \( -17 a^{3} + \frac{11}{2} a^{2} + \frac{329}{2} a + 180\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-\frac{7}{2}a-4\right){x}{y}+\left(\frac{1}{2}a^{3}-\frac{1}{2}a^{2}-3a\right){y}={x}^{3}+\left(-\frac{1}{2}a^{2}+\frac{3}{2}a+3\right){x}^{2}+\left(\frac{11}{2}a^{3}-3a^{2}-\frac{83}{2}a-34\right){x}-17a^{3}+\frac{11}{2}a^{2}+\frac{329}{2}a+180$ |
| 20.1-b5 |
20.1-b |
$6$ |
$8$ |
4.4.19025.1 |
$4$ |
$[4, 0]$ |
20.1 |
\( 2^{2} \cdot 5 \) |
\( 2^{4} \cdot 5^{2} \) |
$17.92378$ |
$(-1/2a^3+3/2a^2+3a-9), (1/2a^3-7/2a-1)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$596.9953138$ |
1.082053160 |
\( -61855209786 a^{3} - \frac{914444045557}{20} a^{2} + \frac{3394381673572}{5} a + \frac{4967961465243}{5} \) |
\( \bigl[\frac{1}{2} a^{2} + \frac{1}{2} a - 4\) , \( -\frac{1}{2} a^{3} + \frac{7}{2} a + 5\) , \( 0\) , \( 57 a^{3} - 214 a^{2} - 373 a + 1463\) , \( \frac{641}{2} a^{3} - \frac{2397}{2} a^{2} - 2086 a + 8123\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{2}+\frac{1}{2}a-4\right){x}{y}={x}^{3}+\left(-\frac{1}{2}a^{3}+\frac{7}{2}a+5\right){x}^{2}+\left(57a^{3}-214a^{2}-373a+1463\right){x}+\frac{641}{2}a^{3}-\frac{2397}{2}a^{2}-2086a+8123$ |
| 20.1-b6 |
20.1-b |
$6$ |
$8$ |
4.4.19025.1 |
$4$ |
$[4, 0]$ |
20.1 |
\( 2^{2} \cdot 5 \) |
\( 2^{8} \cdot 5^{4} \) |
$17.92378$ |
$(-1/2a^3+3/2a^2+3a-9), (1/2a^3-7/2a-1)$ |
0 |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$1$ |
$596.9953138$ |
1.082053160 |
\( \frac{39960753}{200} a^{3} + \frac{144939693}{400} a^{2} - \frac{253145487}{200} a - \frac{224436463}{100} \) |
\( \bigl[\frac{1}{2} a^{3} - \frac{1}{2} a^{2} - 4 a + 1\) , \( -\frac{1}{2} a^{3} + \frac{1}{2} a^{2} + 4 a\) , \( 1\) , \( -4 a^{3} - \frac{9}{2} a^{2} + \frac{65}{2} a + 46\) , \( -\frac{21}{2} a^{3} - 16 a^{2} + \frac{159}{2} a + 131\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-\frac{1}{2}a^{2}-4a+1\right){x}{y}+{y}={x}^{3}+\left(-\frac{1}{2}a^{3}+\frac{1}{2}a^{2}+4a\right){x}^{2}+\left(-4a^{3}-\frac{9}{2}a^{2}+\frac{65}{2}a+46\right){x}-\frac{21}{2}a^{3}-16a^{2}+\frac{159}{2}a+131$ |
| 20.2-a1 |
20.2-a |
$4$ |
$4$ |
4.4.19025.1 |
$4$ |
$[4, 0]$ |
20.2 |
\( 2^{2} \cdot 5 \) |
\( 2^{2} \cdot 5^{4} \) |
$17.92378$ |
$(1/2a^3+1/2a^2-6a-9), (1/2a^3-7/2a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 2^{2} \) |
$1$ |
$67.28192121$ |
1.951174190 |
\( \frac{5491064807}{50} a^{3} - \frac{21026701137}{50} a^{2} - \frac{7035355141}{10} a + \frac{71749945762}{25} \) |
\( \bigl[\frac{1}{2} a^{2} + \frac{1}{2} a - 3\) , \( \frac{1}{2} a^{2} + \frac{1}{2} a - 5\) , \( \frac{1}{2} a^{3} - \frac{1}{2} a^{2} - 3 a + 1\) , \( -66 a^{3} + 240 a^{2} + 430 a - 1621\) , \( -\frac{1695}{2} a^{3} + \frac{6233}{2} a^{2} + 5515 a - 21072\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{2}+\frac{1}{2}a-3\right){x}{y}+\left(\frac{1}{2}a^{3}-\frac{1}{2}a^{2}-3a+1\right){y}={x}^{3}+\left(\frac{1}{2}a^{2}+\frac{1}{2}a-5\right){x}^{2}+\left(-66a^{3}+240a^{2}+430a-1621\right){x}-\frac{1695}{2}a^{3}+\frac{6233}{2}a^{2}+5515a-21072$ |
| 20.2-a2 |
20.2-a |
$4$ |
$4$ |
4.4.19025.1 |
$4$ |
$[4, 0]$ |
20.2 |
\( 2^{2} \cdot 5 \) |
\( 2^{4} \cdot 5^{2} \) |
$17.92378$ |
$(1/2a^3+1/2a^2-6a-9), (1/2a^3-7/2a-1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$1$ |
$1076.510739$ |
1.951174190 |
\( 2012 a^{3} - \frac{175599}{20} a^{2} - \frac{59482}{5} a + \frac{322844}{5} \) |
\( \bigl[\frac{1}{2} a^{2} + \frac{1}{2} a - 3\) , \( \frac{1}{2} a^{2} + \frac{1}{2} a - 5\) , \( \frac{1}{2} a^{3} - \frac{1}{2} a^{2} - 3 a + 1\) , \( -\frac{7}{2} a^{3} + 15 a^{2} + \frac{45}{2} a - 101\) , \( -\frac{19}{2} a^{3} + \frac{75}{2} a^{2} + 62 a - 256\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{2}+\frac{1}{2}a-3\right){x}{y}+\left(\frac{1}{2}a^{3}-\frac{1}{2}a^{2}-3a+1\right){y}={x}^{3}+\left(\frac{1}{2}a^{2}+\frac{1}{2}a-5\right){x}^{2}+\left(-\frac{7}{2}a^{3}+15a^{2}+\frac{45}{2}a-101\right){x}-\frac{19}{2}a^{3}+\frac{75}{2}a^{2}+62a-256$ |
| 20.2-a3 |
20.2-a |
$4$ |
$4$ |
4.4.19025.1 |
$4$ |
$[4, 0]$ |
20.2 |
\( 2^{2} \cdot 5 \) |
\( 2^{8} \cdot 5 \) |
$17.92378$ |
$(1/2a^3+1/2a^2-6a-9), (1/2a^3-7/2a-1)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$1076.510739$ |
1.951174190 |
\( -\frac{11779}{40} a^{3} - \frac{7275}{16} a^{2} + \frac{141277}{40} a + \frac{167649}{20} \) |
\( \bigl[\frac{1}{2} a^{2} + \frac{1}{2} a - 3\) , \( -\frac{1}{2} a^{3} + \frac{1}{2} a^{2} + 5 a\) , \( \frac{1}{2} a^{3} - \frac{7}{2} a - 3\) , \( -\frac{3}{2} a^{3} + a^{2} + \frac{25}{2} a + 14\) , \( -a^{3} + a^{2} + 9 a + 7\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{2}+\frac{1}{2}a-3\right){x}{y}+\left(\frac{1}{2}a^{3}-\frac{7}{2}a-3\right){y}={x}^{3}+\left(-\frac{1}{2}a^{3}+\frac{1}{2}a^{2}+5a\right){x}^{2}+\left(-\frac{3}{2}a^{3}+a^{2}+\frac{25}{2}a+14\right){x}-a^{3}+a^{2}+9a+7$ |
| 20.2-a4 |
20.2-a |
$4$ |
$4$ |
4.4.19025.1 |
$4$ |
$[4, 0]$ |
20.2 |
\( 2^{2} \cdot 5 \) |
\( 2^{2} \cdot 5 \) |
$17.92378$ |
$(1/2a^3+1/2a^2-6a-9), (1/2a^3-7/2a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$1076.510739$ |
1.951174190 |
\( -\frac{617909}{10} a^{3} + \frac{644489}{2} a^{2} + \frac{339727}{10} a - \frac{6203406}{5} \) |
\( \bigl[\frac{1}{2} a^{3} - \frac{1}{2} a^{2} - 3 a + 1\) , \( \frac{1}{2} a^{3} - \frac{1}{2} a^{2} - 4 a - 1\) , \( \frac{1}{2} a^{3} - \frac{9}{2} a - 3\) , \( \frac{19}{2} a^{3} - 49 a^{2} + \frac{13}{2} a + 210\) , \( -49 a^{3} + 346 a^{2} - 152 a - 1569\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-\frac{1}{2}a^{2}-3a+1\right){x}{y}+\left(\frac{1}{2}a^{3}-\frac{9}{2}a-3\right){y}={x}^{3}+\left(\frac{1}{2}a^{3}-\frac{1}{2}a^{2}-4a-1\right){x}^{2}+\left(\frac{19}{2}a^{3}-49a^{2}+\frac{13}{2}a+210\right){x}-49a^{3}+346a^{2}-152a-1569$ |
| 20.2-b1 |
20.2-b |
$2$ |
$2$ |
4.4.19025.1 |
$4$ |
$[4, 0]$ |
20.2 |
\( 2^{2} \cdot 5 \) |
\( - 2^{4} \cdot 5^{2} \) |
$17.92378$ |
$(1/2a^3+1/2a^2-6a-9), (1/2a^3-7/2a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.223899094$ |
$585.6183105$ |
3.802459906 |
\( \frac{12071}{40} a^{3} + \frac{20413}{40} a^{2} - \frac{45141}{20} a - \frac{38721}{10} \) |
\( \bigl[\frac{1}{2} a^{3} - \frac{9}{2} a - 3\) , \( -\frac{1}{2} a^{2} - \frac{1}{2} a + 5\) , \( \frac{1}{2} a^{3} - \frac{9}{2} a - 4\) , \( -2 a^{3} - 5 a^{2} + 14 a + 38\) , \( 6 a^{3} + 8 a^{2} - 44 a - 63\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{3}-\frac{9}{2}a-3\right){x}{y}+\left(\frac{1}{2}a^{3}-\frac{9}{2}a-4\right){y}={x}^{3}+\left(-\frac{1}{2}a^{2}-\frac{1}{2}a+5\right){x}^{2}+\left(-2a^{3}-5a^{2}+14a+38\right){x}+6a^{3}+8a^{2}-44a-63$ |
| 20.2-b2 |
20.2-b |
$2$ |
$2$ |
4.4.19025.1 |
$4$ |
$[4, 0]$ |
20.2 |
\( 2^{2} \cdot 5 \) |
\( - 2^{2} \cdot 5 \) |
$17.92378$ |
$(1/2a^3+1/2a^2-6a-9), (1/2a^3-7/2a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$0.447798189$ |
$1171.236621$ |
3.802459906 |
\( -\frac{133021}{20} a^{3} - \frac{36099}{4} a^{2} + \frac{377872}{5} a + \frac{752378}{5} \) |
\( \bigl[1\) , \( -\frac{1}{2} a^{2} - \frac{1}{2} a + 5\) , \( \frac{1}{2} a^{3} - \frac{7}{2} a - 4\) , \( -20 a^{3} + \frac{149}{2} a^{2} + \frac{259}{2} a - 501\) , \( \frac{239}{2} a^{3} - \frac{897}{2} a^{2} - 776 a + 3032\bigr] \) |
${y}^2+{x}{y}+\left(\frac{1}{2}a^{3}-\frac{7}{2}a-4\right){y}={x}^{3}+\left(-\frac{1}{2}a^{2}-\frac{1}{2}a+5\right){x}^{2}+\left(-20a^{3}+\frac{149}{2}a^{2}+\frac{259}{2}a-501\right){x}+\frac{239}{2}a^{3}-\frac{897}{2}a^{2}-776a+3032$ |
*The rank, regulator and analytic order of Ш are
not known for all curves in the database; curves for which these are
unknown will not appear in searches specifying one of these
quantities.
